Directional ratio based on parabolic molecules and its application to the analysis of tubular structures

Demetrio Labate, Pooran Negi, Burcin Ozcan, Manos Papadakis, Manos Papadakis, Vivek K. Goyal, Dimitri Van De Ville
2015 Wavelets and Sparsity XVI  
As advances in imaging technologies make more and more data available for biomedical applications, there is an increasing need to develop efficient quantitative algorithms for the analysis and processing of imaging data. In this paper, we introduce an innovative multiscale approach called Directional Ratio which is especially effective to distingush isotropic from anisotropic structures. This task is especially useful in the analysis of images of neurons, the main units of the nervous systems
more » ... ich consist of a main cell body called the soma and many elongated processes called neurites. We analyze the theoretical properties of our method on idealized models of neurons and develop a numerical implementation of this approach for analysis of fluorescent images of cultured neurons. We show that this algorithm is very effective for the detection of somas and the extraction of neurites in images of small circuits of neurons. Obviously the scale at which the isotropy is observed is not unique. For example, let A be a ball of radius S > 0. Then the ball at its center is locally isotropic at any radius up to scale 2S. Our definition above attempts to establish a connection
doi:10.1117/12.2186259 fatcat:sfijcgjzyfgydfd3sn7kvmvueq